# Daniel's triple challenge

Algebra Level 5

How many ordered triples of complex numbers $$(a, b, c)$$ are there such that $$a^3-b$$, $$b^3-c$$, and $$c^3-a$$ are rational numbers, and

$a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2(a^3b+b^3c+c^3a)?$

This problem is posed by Daniel C.

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